Answer:
28
Step-by-step explanation:
If 50% of students are boys that means there are 30 boys and 30 girls. Then if 30% of boys are 10 and 60% of girls are 18. You add 18+10 and that gives you 28.
I would pick the “D” the same line
Hey there!
We can solve inequalities just like equations. There is only one difference though. If you ever multiply or divide both sides by a negative number, you "flip" the inequality sign.
First, let's undo the parentheses.
2x-24+24<4x+20
We simplify.
2x<4x+20
We subtract 4x from both sides.
-2x<20
We divide both sides by -2 (we will need to flip the inequality sign).
x>-10
I hope this helps!
Answer:
a) 0.857
b) 0.571
c) 1
Step-by-step explanation:
Based on the data given, we have
- 18 juniors
- 10 seniors
- 6 female seniors
- 10-6 = 4 male seniors
- 12 junior males
- 18-12 = 6 junior female
- 6+6 = 12 female
- 4+12 = 16 male
- A total of 28 students
The probability of each union of events is obtained by summing the probabilities of the separated events and substracting the intersection. I will abbreviate female by F, junior by J, male by M, senior by S. We have
- P(J U F) = P(J) + P(F) - P(JF) = 18/28+12/28-6/28 = 24/28 = 0.857
- P(S U F) = P(S) + P(F) - P(SF) = 10/28 + 12/28 - 6/28 = 16/28 = 0.571
- P(J U S) = P(J) + P(S) - P(JS) = 18/28 + 10/28 - 0 = 1
Note that a student cant be Junior and Senior at the same time, so the probability of the combined event is 0. The probability of the union is 1 because every student is either Junior or Senior.
Answer:
15cm by 20cm by 25cm
Step-by-step explanation:
Let the sides of the right angle be x, y and h
x is the breadth
y is the height
h is the hypotenuse
Perimeter = x + y + h
x + y +h = 60
x+y = 60-h .... 1
If its area is equal to 150 square cm, then;
Area = 1/2 * base * height
Area = 1/2 *x * y
xy/2 = 150
xy = 300 ....2
According to pythagoras theorem;
x² + y² = h²
On expanding x² + y²
x² + y² = (x+y)² - 2xy
The equation becomes
(x+y)² - 2xy = h² ... 3
Substitute equation 1 and 2 into 3;
From 3;
(x+y)² - 2xy = h² ... 3
(60-h)² - 2(300) = h²
3600-120h + h² - 600 = h²
3600-120h - 600 = 0
-120h = 600-3600
-120h = -3000
h = 3000/120
h = 25cm
Recall that x+y+h = 60
x+y+25 = 60
x+y = 60 - 25
x+y = 35 ... 4
From equation 2;
xy = 300
x = 300/y ..... 5
Substitute 5 into 4;
300/y + y = 35
(300+y²)/y = 35
300+y² = 35y
y²-35y + 300 = 0
y²-20y-15y + 300 = 0
y(y-20)-15(y-20) = 0
y-20 = 0 and y - 15 =0
y = 20 and 15
since x+y = 35
x + 20 = 35
x = 35 - 20
x = 15
Hence the sides of the triangle are 15cm by 20cm by 25cm
